Wind gusts create ripples on the ocean that have a wavelength of 5.00 cm and propagate at 2.00 m/s. What is their frequency

Answer:

Mass of shot (m) = 4 kg

Explanation:

Given:

Velocity (v) = 15 m/s

Mechanical kinetic energy (K.E) = 450 J

Find:

Mass of shot (m) = ?

Computation:

Mechanical kinetic energy (K.E) = 1/2mv²

Mechanical kinetic energy (K.E) = [1/2](m)(15)²

450 = [1/2](m)(15)²

900 = 225 m

Mass of shot (m) = 4 kg

Answer:

 x = 0.006 m

Explanation:

The potential at one point is given by

          V = k ∑ [tex]q_{i} / r_{i}[/tex]

remember that the potential is to scale, let's apply to our case

          V = k (q₁ / x₁ + q₂ / x₂ + q₃ / x)

in this case they indicate that the potential is zero

          0 = k (2 10⁻⁶ / (- 1 10⁻²) + (-6 10⁻⁶) / 2 10⁻² + ​​3 10⁻⁶ / x)

         3 / x = + 2 / 10⁻² + ​​3 / 10⁻²

         3 / x = 500

          x = 3/500

          x = 0.006 m

Answer:

2.64 x 10⁻⁶T

Explanation:

The magnitude of the magnetic field produced by a long straight wire carrying current is given by Biot-Savart law as follows: "The magnetic field strength is directly proportional to the current on the wire and inversely proportional to the distance from the wire". This can be written mathematically as;

B = (μ₀ I) / (2π r)                ----------------(i)

B is magnetic field

I is current through the wire

r is the distance from the wire

μ₀  is the magnetic constant = 4π x 10⁻⁷Hm⁻¹

From the question;

I = 0.7A

r = 0.053m

Substitute these values into equation (i) as follows;

B =  (4π x 10⁻⁷ x 0.7) / (2π x 0.053)

B = 2.64 x 10⁻⁶T

Therefore the approximate magnitude of the magnetic field at that location is 2.64 x 10⁻⁶T

Answer:

The mass of the object is 745000 units of the sun

Explanation:

We know that the centripetal force with which the stars orbit the object is represented as

[tex]F_{c}[/tex] = [tex]\frac{mv^{2} }{r}[/tex]

and this centripetal force is also proportional to

[tex]F_{c}[/tex] = [tex]\frac{kMm}{r^{2} }[/tex]

where

m is the mass of the stars

M is the mass of the object

v is the velocity of the stars = 10^6 m/s

r is the distance between the stars and the object = 10^14 m

k is the gravitational constant = 6.67 × 10^-11 m^3 kg^-1 s^-2

We can equate the two centripetal force equations to give

[tex]\frac{mv^{2} }{r}[/tex] = [tex]\frac{kMm}{r^{2} }[/tex]

which reduces to

[tex]v^{2}[/tex] = [tex]\frac{kM}{r}[/tex]

and then finally

M = [tex]\frac{rv^{2} }{k}[/tex]

substituting values, we have

M = [tex]\frac{10^{14}*(10^{6})^{2} }{6.67*10^{-11} }[/tex] = 1.49 x 10^36 kg

If the mass of the sun is 2 x 10^30 kg

then, the mass of the the object in units of the mass of the sun is

==> (1.49 x 10^36)/(2 x 10^30) = 745000 units of sun

Answer:

   s_400 = 16.5 m , s_700 = 29.4 m

Explanation:

The limit of the human eye's solution is determined by the diffraction limit that is given by the expression

                   θ = 1.22 λ / D

where you lick the wavelength and D the mediator of the circular aperture.

In our case, the dilated pupil has a diameter of approximately 8 mm = 8 10-3 m and the eye responds to a wavelength between 400 nm and 700 nm.

by introducing these values ​​into the formula

λ = 400 nm      θ = 1.22 400 10⁻⁹ / 8 10⁻³ = 6 10⁻⁵ rad

λ = 700 nm     θ = 1.22 700 10⁻⁹ / 8 10⁻³-3 = 1.07 10⁻⁴ rad

Now we can use the definition radians

          θ= s / R

where s is the supported arc and R is the radius. Let's find the sarcos for each case

λ = 400 nm       s_400 = θ R

                         S_400 = 6 10⁻⁵ 275 10³

                         s_400 = 16.5 m

λ = 700 nm s_ 700 = 1.07 10⁻⁴ 275 10³

                          s_700 = 29.4 m

Answer:

The 50N weight be hung  at 23 cm to maintain equilibrium

Explanation:

Given;

length of the uniform rod = 30 cm

center of the uniform rod = 15 cm

weight of 40N is hung at 5 cm mark

weight of 50 N will be hung at ?

     0------5cm-----------------15cm-------------P---------30cm

              ↓             10cm      Δ       xcm    ↓

             40N                                             50N

Take moment about the pivot point and apply the principle of moment

50N (x cm) = 40N (10 cm)

x = (400) / 50

x = 8cm

P = x cm + 15 cm

P = 8 cm + 15 cm

P = 23 cm

Therefore, the 50N weight be hung  at 23 cm to maintain equilibrium

Answer:

1248m

The time that wave moves from the wave source to the ocean floor is half the total travel time: t = 2.5/2 = 1.25s

The speed of sound in seawater is 1560 m/s

Therefore, s = vt = (1560 m/s)(1.25s) =1248 m = 1.2km

Answer:

Heat Flow Rate : ( About ) 87 W

Explanation:

The heat flowing out of the system each minute, will be represented by the following equation,

Q( cup ) + Q( water ) = m( cup ) [tex]*[/tex] c( al ) [tex]*[/tex] ΔT + m( w ) [tex]*[/tex] c( w ) [tex]*[/tex] ΔT

So as you can see, the mass of the aluminum cup is 150 grams. For convenience, let us convert that into kilograms,

150 grams = .15 kilograms - respectively let us convert the mass of water to kilograms,

800 grams = .8 kilograms

Now remember that the specific heat of aluminum is 900 J / kg [tex]*[/tex] K, and the specific heat of water = 4186 J / kg [tex]*[/tex] K. Therefore let us solve for " the heat flowing out of the system per minute, "

Q( cup ) + Q( water ) = .15 [tex]*[/tex] ( 900 J / kg [tex]*[/tex] K )  [tex]*[/tex] 1.5 + .8 [tex]*[/tex] ( 4186 J / kg [tex]*[/tex] K ) [tex]*[/tex] 1.5,

Q( cup ) + Q( water ) = 5225.7 Joules

And the heat flow rate should be Joules per minute,

5225.7 Joules / 60 seconds = ( About ) 87 W

Answer:

w = √ 1 / CL

This does not violate energy conservation because the voltage of the power source is equal to the voltage drop in the resistence

Explanation:

This problem refers to electrical circuits, the circuits where this phenomenon occurs are series RLC circuits, where the resistor, the capacitor and the inductance are placed in series.

In these circuits the impedance is

             X = √ (R² +  ([tex]X_{C}[/tex] -[tex]X_{L}[/tex])² )

where Xc and XL is the capacitive and inductive impedance, respectively

            X_{C} = 1 / wC

           X_{L} = wL

From this expression we can see that for the resonance frequency

           X_{C} = X_{L}

the impedance of the circuit is minimal, therefore the current and voltage are maximum and an increase in signal intensity is observed.

This does not violate energy conservation because the voltage of the power source is equal to the voltage drop in the resistence

               V = IR

Since the contribution of the two other components is canceled, this occurs for

                X_{C} = X_{L}

                1 / wC = w L

                w = √ 1 / CL

Answer:

So, according to Einstein's special relativity a person on Mars observe the light to be traveling at c = 3 x 10⁸ m/s.

Explanation:

The special theory of relativity has two main postulates:

1- VALIDITY OF PHYSICAL LAWS

The laws of physics such as Newton's Laws and Maxwell's Equations are valid in all inertial frame of references.

2- CONSTANCY OF SPEED OF LIGHT

The speed of light in vacuum is the same for all observers in uniform translational relative motion, and it is independent of the motion of the source or the observer. Thus, speed of light is a universal constant and its value is c = 3 x 10⁸ m/s.

So, according to Einstein's special relativity a person on Mars observe the light to be traveling at c = 3 x 10⁸ m/s.

Answer:

OPTION B is correct

Carbon

Explanation:

element can be defined as a pure substance which cannot be broken down by into smaller units through a chemical method, an element has atoms with identical numbers of protons in their atomic nuclei

Each element is composed of its own type of atom. And this gives the reason why chemical elements are all very different from each other. And all substance on Earth has atoms of at least one of this elements.

There about 118 elements and all arranged in a row and colomn of the periodic table .This elements of the periodic table are arranged by their atomic number, which helps with the chemical properties. Example of elements are; Hydrogen, Oxygeñ, carbon.

Therefore, among the option only carbon is an element because it cannot be broken down into smaller unit unlike water which is made up of oxygen and hydrogen. Also salt is a compound containing more elements.

The substance which represents an element given the following option is carbon (option B)

An element is a pure substance that consist of identical atoms.

An element can not be broken down into simple substances by ordinary methods.

The period table consist of a large number of elements. Some of which are:

We must also understand that when two or more elements are chemically combined together it is called a compound and when they are not chemically combined together, it is called a mixture.

Thus, we can conclude that the correct answer to the question is Carbon (option B)

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Answer:

Since their wings and body develop the drag. When there is warm air then they expand their wings. Since,soaring birds and glider pilots have no engine, they always maintain their high speed to lift their weight in air for hours without expending power by convection

Explanation:

Answer:

ω = 12.023 rad/s

α = 222.61 rad/s²

Explanation:

We are given;

ω0 = 2.37 rad/s, t = 0 sec

ω =?, t = 0.22 sec

α =?

θ = 57°

From formulas,

Tangential acceleration; a_t = rα

Normal acceleration; a_n = rω²

tan θ = a_t/a_n

Thus; tan θ = rα/rω² = α/ω²

tan θ = α/ω²

α = ω²tan θ

Now, α = dω/dt

So; dω/dt = ω²tan θ

Rearranging, we have;

dω/ω² = dt × tan θ

Integrating both sides, we have;

(ω, ω0)∫dω/ω² = (t, 0)∫dt × tan θ

This gives;

-1[(1/ω_o) - (1/ω)] = t(tan θ)

Thus;

ω = ω_o/(1 - (ω_o × t × tan θ))

While;

α = dω/dt = ((ω_o)²×tan θ)/(1 - (ω_o × t × tan θ))²

Thus, plugging in the relevant values;

ω = 2.37/(1 - (2.37 × 0.22 × tan 57))

ω = 12.023 rad/s

Also;

α = (2.37² × tan 57)/(1 - (2.37 × 0.22 × tan 57))²

α = 8.64926751525/0.03885408979 = 222.61 rad/s²

Answer:

R' = R/2

Therefore, the new resistance of the wire is twice the value of the initial resistance.

Explanation:

Consider a wire with:

Resistance = R

Length = L

Area = A = πr²

where, r = radius

ρ = resistivity

Then:

R = ρL/A

R = ρL/πr²   --------------- equation 1

Now, the new wire has:

Resistance = R'

Resistivity = ρ

Length = L' = 2 L

Radius = r' = 2r

Area = πr'² = π(2r)² = 4πr²

Therefore,

R' = ρL'/πr'²

R' = ρ(2 L)/4πr²

R' = (1/2)(ρL/πr²)

using equation 1:

R' = R/2

Therefore, the new resistance of the wire is twice the value of the initial resistance.

Answer:

e)

Explanation:

In an RC series circuit, at any time, the sum of the voltages through the resistor and the capacitor must be constant and equal to the voltage of the DC voltage source, in order to be compliant with KVL.

At= 0, as the voltage through the capacitor can't change instantaneously, all the voltage appears through the resistor, which means that a current flows, that begins to charge the capacitor, up to a point that the voltage through the capacitor is exactly equal to the DC voltage, so no current flows in the circuit anymore, and the charge in the capacitor reaches to its maximum value.

Answer:

4.9x10^-6T

Explanation:

See attached file

Answer:

D. 0.1

Explanation:

Using transformer equation,

N2/N1 = I1/I2................... Equation 1

Where N2 = secondary coil, N1 = primary coil, I1 = input current, I2 = output current.

make I2  the subject of the equation

I2 = I1/(N2/N1)............ Equation 2

From equation 2 above, For the output current of the secondary coil to be 10 times the input current, N2/N1 = 0.1

Hence the right option is D. 0.1

Answer:

Explanation:

 An insulator is a material that impedes the movement of heat or electric current from flowing.

Theoretically good heat insulators stops the movement of heat, while practically this insulation can only be slowed down.

Hence from the options listed the correct answer practically is

Answer:

The magnitude of the magnetic field is 55μT

Explanation:

Given;

number of turns of the solenoid per length, n = N/L = 1500 turns/m

current in the solenoid, I = 20 mA = 20 x 10⁻³ A

diameter of the solenoid, d = 4 cm = 0.04 m

The magnetic field at a point that is inside the solenoid;

B₁ = μ₀nI

Where;

μ₀ is permeability of free space = 4π x 10⁻⁷ m/A

B₁ = 4π x 10⁻⁷ x 1500 x 20 x 10⁻³

B₁ = 3.77 x 10⁻⁵ T

Given;

current in the wire, I = 2 A

distance of magnetic field from the wire, r = 1 cm = 0.01 m

The magnetic field at 1.0 cm from the wire;

[tex]B_2 = \frac{\mu_0I}{2\pi r} \\\\B_2 = \frac{4\pi*10^{-7}*2}{2\pi *0.01}\\\\B_2 = 4 *10^{-5} \ T[/tex]

The magnitude of the magnetic field;

[tex]B = \sqrt{B_1^2 +B_2^2} \\\\B = \sqrt{(3.77*10^{-5})^2 + (4*10^{-5})^2} \\\\B = 5.5 *10^{-5} \ T\\\\B = 55 \mu T[/tex]

Therefore, the magnitude of the magnetic field is 55μT

The magnitude of the magnetic field at a point that is inside the solenoid and 1.0 cm from the wire is [tex]5.5 \times 10^{-5}T[/tex]

Given the following parameters from the question  

The magnetic field at a point that is inside the solenoid is expressed according to the formula;  

Where;  

μ₀ is the permeability of free space = 4π x 10⁻⁷ m/A  

B₁ = 4π x 10⁻⁷ x 1500 x 20 x 10⁻³  

B₁ = 3.77 x 10⁻⁵ T

Next is to get the magnetic field strength in the second wire.

Substitute into the formula:

[tex]B_2=\dfrac{\mu_0 I}{2 \pi r} \\B_2=\frac{4\pi \times 10^{-7}\times 2}{2 \times 3.14\times 0.01} \\B_2 =4.0 \times 10^{-5}T[/tex]

Get the resultant magnetic field:

[tex]B = \sqrt{(0.00003771)^2+(0.00004)^2} \\B =5.5 \times 10^{-7}T[/tex]

Therefore the magnitude of the magnetic field at a point that is inside the solenoid and 1.0 cm from the wire is [tex]5.5 \times 10^{-5}T[/tex]

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Answer:

9.42*10^-4 m^3/s

Explanation:

d=3/100 m

=0.03 m

A=3.14*0.03^2/6

=4.71*10^-4 m^2

Volume flow rate V = A * s

= 4.71*10^-4 * 2

= 9.42*10^-4

So, the volume flw rate of fluid is 9.42*10^-4 m^3/s

Answer:

To calculate the predicted surface elevation of a 50km thick crust above a surface of 2.5km we are given a density of 3 gram per centimeter cube.

The displacement of the material will be calculated by subtracting the surface elevation of 2.5 km from the 50 km thick crust. Therefore 50-25= 47.5 km.

Thus let the density of the material be Pm

50*3= 47.5*Pm

Therefore: Pm= (50*3)/47.5= 3.16gram per centimeter cube

Thus with an average density of 2.8gram per centimeter cube

50*2.8= (50-x)*3.16

(50-x)= (50*2.8)/3.16

50-x=44.3

x=50-44.3= 5.7

Explanation:

To calculate the predicted surface elevation of a 50km thick crust above a surface of 2.5km we are given a density of 3 gram per centimeter cube.

The displacement of the material will be calculated by subtracting the surface elevation of 2.5 km from the 50 km thick crust. Therefore 50-25= 47.5 km.

Thus let the density of the material be Pm

50*3= 47.5*Pm

Therefore: Pm= (50*3)/47.5= 3.16gram per centimeter cube

Thus with an average density of 2.8gram per centimeter cube

50*2.8= (50-x)*3.16

(50-x)= (50*2.8)/3.16

50-x=44.3

x=50-44.3= 5.7

Answer:

The cost of the buying the shirts is #9680

Explanation:

let the cost of buying shirt = C

let the number of shirt bought = N

The following equation can be generated based on the statement above;

C = k + Nb

When the cost, C = #240, the number of shirt = 5

240 = k + 5b ------ equation (1)

where;

k and b are constants

When the cost, C = #400, the number of shirt = 10

400 = k + 10b ------ equation (2)

From equation (1), make k the subject of the formula;

k = 240 - 5b ---- equation (3)

Substitute in the value of k into equation (2)

400 = k + 10b

400 = (240 - 5b) + 10b

400 = 240 - 5b + 10b

400 - 240 = -5b + 10b

160 = 5b

b = 160 / 5

b = 32

From equation (3), calculate k

k = 240 - 5b

k = 240 -5(32)

k = 240 - 160

k = 80

When the number of shirts bought = 300, the cost of the buying the shirts =

C =  k + Nb

C = 80 +32N

Where;

N is the number of shirts

C = 80 + 32(300)

C = 80 + 9600

C = #9680

Therefore, the cost of the buying the shirts is #9680

Answer:

V = 451.47 volts

Explanation:

Given that,

Distance, d = 0.21 m

Initial speed, u = 0

Time, t = 33.3 ns

Let v is the final velocity. Using second equation of motion as :

[tex]d=ut+\dfrac{1}{2}at^2[/tex]

a is acceleration, [tex]a=\dfrac{v-u}{t}[/tex] and u = 0

So,

[tex]d=\dfrac{1}{2}(v-u)t[/tex]

[tex]v=\dfrac{2d}{t}\\\\v=\dfrac{2\times 0.21}{33.3\times 10^{-9}}\\\\v=1.26\times 10^7\ m/s[/tex]

Now applying the conservation of energy i.e.

[tex]\dfrac{1}{2}mv^2=qV[/tex]

V is voltage

[tex]V=\dfrac{mv^2}{2q}\\\\V=\dfrac{9.1\times 10^{-31}\times (1.26\times 10^7)^2}{2\times 1.6\times 10^{-19}}\\\\V=451.47\ V[/tex]

So, the voltage is 451.47 V.

Answer:

 v ’= 21.44 m / s

Explanation:

This is a doppler effect exercise that changes the frequency of the sound due to the relative movement of the source and the observer, the expression that describes the phenomenon for body approaching s

           f ’= f (v + v₀) / (v-[tex]v_{s}[/tex])

where it goes is the speed of sound 343 m / s, v_{s} the speed of the source v or the speed of the observer

in this exercise both the source and the observer are moving, we will assume that both have the same speed,

                v₀ = v_{s} = v ’

we substitute

               f ’= f (v + v’) / (v - v ’)

               f ’/ f (v-v’) = v + v ’

               v (f ’/ f -1) = v’ (1 + f ’/ f)

               v ’= (f’ / f-1) / (1 + f ’/ f) v

               v ’= (f’-f) / (f + f’) v

let's calculate

                v ’= (3400 -3000) / (3000 +3400) 343

                v ’= 400/6400 343

                v ’= 21.44 m / s

Answer:

The 1/2 inch barrel will burst at the same height of 20 ft

Explanation:

The pressure on a column of fluid increases with depth, and decreases with height. This means that if you increase the height of the fluid in the column, the pressure at the bottom will increase.

From the equation of fluid pressure,

P = ρgh

where

P is the pressure at the bottom of the fluid due to its height

ρ is the density of the fluid in question

h is the height to which the water stand.

You notice how apart from the height 'h' in the equation, all the other parts of the right hand side of the equation cannot be varied; they are a fixed property of the fluid and gravity. And there is no consideration for the horizontal diameter of the water's cross section area.

We can also think of the pressure at the bottom of the fluid to be as a result of an incremental weight of an infinitesimally small vertical section of the water down.

That been said, we can then say that if the barrel with the 1 ft diameter dimension bursts when filled with water up to 20 ft, then, the barrel with the reduced diameter will still burst at the same height as the former pipe.

NB: The only way to stop the pipe from bursting is to increase the thickness of the barrel wall to counteract the pressure forces due to the height.

Answer:

The speed of the ball relative to the ground if the ball is thrown forward is 58.1 m/s

Explanation:

Given;

speed of the ball thrown inside boxcar, [tex]V_B[/tex] = 23.2 m/s

speed of the boxcar moving along the tracks, [tex]V_T[/tex] = 34.9 m/s

Determine the speed of the ball relative to the ground if the ball is thrown forward.

If the ball is thrown forward, the speed of the ball relative to the ground will be sum of the ball's speed plus speed of the boxcar.

[tex]V_{relative \ speed} = V_B + V_T\\\\V_{relative \ speed} = 23.2 + 34.9\\\\V_{relative \ speed} = 58.1 \ m/s[/tex]

Therefore,  the speed of the ball relative to the ground if the ball is thrown forward is 58.1 m/s.

Answer:

It will neither translate in the opposite direction nor .rotate so as to be at right angles, it will also neither rotate so as to be vertical direction

Answer:

I think the answer probably be B

What explains why a prism separates white light into a light spectrum ?

C. The different colors that make up a white light have different refractive indexes in glass.

✔ Indeed, depending on the radiation (and therefore colors), which each have different wavelengths, the refraction index varies: the larger the wavelength (red) the less the reflection index is important and vice versa (purple).

✔ That's why purple is more deflected so is lower than red radiation.  

Answer:

The acceleration is  [tex]a = 2.190 *10^{-7} \ m/s^2[/tex]

Explanation:

From the question we are told that

      The  distance of separation of the ship is  [tex]r= 109 \ m[/tex]

       The mass of each ship is  [tex]M = 39,000 \ metric\ tons =39,000 * 1000 = 3.9 *10^{7}\ kg[/tex]

The gravitational force of attraction exerted on each other is mathematically represented as

            [tex]F_g = \frac{ GMM}{r^2}[/tex]

Where G is the gravitational  constant with value

substituting values

          [tex]F_g = \frac{ 6.674 30 * 10^{-11} (3.9 *10^{7})^2}{109^2}[/tex]

         [tex]F_g = 8.54 \ N[/tex]

This force can also be mathematically represented as

        [tex]F_g = M * a[/tex]

=>   [tex]a = \frac{F_g}{M}[/tex]

substituting values

     [tex]a = \frac{8.544}{3.9 *10^{7}}[/tex]

     [tex]a = 2.190 *10^{-7} \ m/s^2[/tex]